Fractional order PID controller design based on Laguerre orthogonal functions

Abstract

This paper proposes a novel fractional order PID controller for commensurate fractional order systems based on Laguerre orthonormal functions. The transfer functions of the fractional order plant, the desired loop gain and the fractional order PID controller are expanded in terms of their Laguerre basis functions. Matching the first three coefficients of the Laguerre series of the loop gain with the desired one yields the fractional order PID controller parameters. The pole of the fractional order Laguerre basis function is adjusted to minimize an integral square error performance index subject to control signal constraint. The numerical examples are presented to show the effectiveness of this Laguerre based fractional order PID controller.